A238708 Number of strict partitions of n that include a pair of consecutive integers.

0, 0, 0, 1, 0, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 13, 15, 19, 23, 28, 33, 41, 48, 58, 68, 81, 95, 113, 131, 154, 179, 209, 241, 281, 323, 374, 429, 494, 565, 649, 739, 845, 961, 1095, 1241, 1411, 1595, 1807, 2039, 2303, 2593, 2923, 3283, 3691, 4139, 4643, 5195

Offset

0,8

Comments

Column 2 of the array at A238709.

Column k=1 of A238354. - Alois P. Heinz, May 02 2014

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Formula

a(n) = A000009(n) - A003114(n). - George Beck, Jan 01 2022

Example

a(10) = 4 counts these partitions: 721, 541, 532, 4321.

Mathematica

PartitionsQ[Range[50]] - Table[Count[IntegerPartitions[n], p_ /; Min[p] >= Length[p]], {n, 50}]

Crossrefs

Cf. A238709, A000009, A238354.

Sequence in context: A017979 A140881 A316081 * A266751 A063827 A241651

Adjacent sequences: A238705 A238706 A238707 * A238709 A238710 A238711

Keyword

nonn,easy

Author

Clark Kimberling, Mar 03 2014

Status

approved